Related papers: Probabilistic Eigensolver with a Trapped-Ion Quant…
Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
To gain deeper insight into the dynamics of complex quantum systems we need a quantum leap in computer simulations. We can not translate quantum behaviour arising with superposition states or entanglement efficiently into the classical…
In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time dependent Hamiltonian. I show that to succeed using AQC, the…
The arithmetic problem of factoring an integer $N$ can be translated into the physics of a quantum device, a result that supports P\'olya's and Hilbert's conjecture to prove Riemann's hypothesis. The energies of this system, being…
The quantum mechanical expression relating two commuting operators is reformulated such that the power method (also called method of moments) for iteratively calculating eigenvalues and eigenvectors becomes applicable. The new iterative…
Simulating plasma physics on quantum computers is difficult because most problems of interest are nonlinear, but quantum computers are not naturally suitable for nonlinear operations. In weakly nonlinear regimes, plasma problems can be…
We study a hardware-efficient variational quantum algorithm ansatz tailored for the trapped-ion quantum simulator, HEA-TI. We leverage programmable single-qubit rotations and global spin-spin interactions among all ions, reducing the…
Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…
Over the last few decades, quantum chemistry has progressed through the development of computational methods based on modern digital computers. However, these methods can hardly fulfill the exponentially-growing resource requirements when…
We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.
We present a hybrid quantum-classical algorithm to simulate thermal states of a classical Hamiltonians on a quantum computer. Our scheme employs a sequence of locally controlled rotations, building up the desired state by adding qubits one…
The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational…
Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenvalue problems $Hv = \lambda v$, such as those occurring in quantum chemistry. It is natural to ask whether the same technique can be applied to…
It is well known in quantum optics that any process involving the preparation of a multimode gaussian state, followed by a gaussian operation and gaussian measurements, can be efficiently simulated by classical computers. Here, we provide…
In recent years, the number of hybrid algorithms that combine quantum and classical computations has been continuously increasing. These two approaches to computing can mutually enhance each others' performances thus bringing the promise of…
With the advent of near-term quantum computers, the simulation of properties of solids using quantum algorithms becomes possible. By an adequate description of the system's Hamiltonian, variational methods enable to fetch the band structure…
Finding eigenstates of a given many-body Hamiltonian is a long-standing challenge due to the perceived computational complexity. Leveraging on the hardware of a quantum computer accommodating the exponential growth of the Hilbert space size…
The variational approach is a cornerstone of computational physics, considering both conventional and quantum computing computational platforms. The variational quantum eigensolver (VQE) algorithm aims to prepare the ground state of a…